1. Field of the Invention
This invention relates generally to voltage comparators, and more specifically to reducing the temperature dependence of a differential voltage comparator.
2. Related Art
FIG. 1 shows a prior art differential voltage comparator 101 used in a current-sensing application in conjunction with a buck converter 103, or step-down DC-to-DC converter, which is a type of switching regulator. In the buck converter 103, a peak current circulating through an external power field-effect transistor (FET) 104 is measured by a small value, high precision, current sense resistor 105, whose resistance varies very little with temperature. The precision of the current sense resistor 105 can be as high as ±0.5%. The value of the peak current is then compared to a fixed reference, thereby limiting a maximum peak current. The value of the differential voltage over the current sense resistor 105 is typically approximately 10-40 mV. The differential voltage comparator 101 comprises an input terminal 111, an input terminal 112 and an output terminal 113. The differential voltage comparator 101 measures a difference between analog voltages Vp and Vm that appear across the current sense resistor 105, which are also present at input terminals 111 and 112, respectively. The differential voltage comparator 101 produces a digital output Vout at the output terminal 113. The differential voltage comparator 101 of FIG. 1, which represents one possible implementation of a differential voltage comparator, comprises a first operational amplifier 115 and a second operational amplifier 116. The trip point, or threshold of comparison, of a differential voltage comparator is a voltage, Vp−Vm, at which the output Vout of the differential voltage comparator changes from high to low, or vice versa. Because of a voltage offset within the first operational amplifier 115, a voltage offset within the second operational amplifier 116 and a mismatch of the resistors 117 and 118, there is a lower limit on the value of the threshold of the differential voltage comparator 101. Differential voltage comparators that are typically found in analog integrated circuits have an internal offset that has a magnitude of approximately 5 mV or approximately 10 mV, and they need a special arrangement to compare a differential voltage with an external fixed reference voltage such as a bandgap voltage, Vref 119.
A differential voltage translinear comparator (hereinafter “translinear comparator”) may be able to operate at a lower threshold than the differential voltage comparator 101. A translinear comparator uses an intrinsic reference that is internal to, and inherent in, the bipolar junction transistors within the translinear comparator. The intrinsic reference is a characteristic voltage of a bipolar junction transistor related to its thermal voltage VT. The relationship between the flow of electrical current and the electrostatic potential across a PN junction depends on the thermal voltage VT, such thatVT=kT/qwhere T is the temperature of the PN junction measured in degrees Kelvin, and q is the magnitude of the electrical charge on an electron (1.602×10−19 Coulombs). The Boltzmann's constant, k, can be expressed as 1.3806×10−23 Joules/degree Kelvin. The thermal voltage VT, and, therefore, the value of the intrinsic reference of a translinear comparator, varies directly proportionately with temperature. Such variation adversely affects the precision of any comparison made by a translinear comparator. The thermal voltage, VT is approximately 25.85 mV at room temperature (approximately 300° K.).
A translinear comparator follows the following relation:
                              V          out                =                  {                                                                      0                  ,                                                            if                      (                                                                        V                          p                                                -                                                  V                          m                                                                    )                                        <                                          aT                      *                                              ln                        ⁡                                                  (                          b                          )                                                                                                                                                                                          1                  ,                                                                          ⁢                                                            if                      ⁡                                              (                                                                              V                            p                                                    -                                                      V                            m                                                                          )                                                              >                                          aT                      *                                              ln                        ⁡                                                  (                          b                          )                                                                                                                                                                            Equation        ⁢                                  ⁢                  (          1          )                    where ‘a’ is a universal physical constant; ‘b’ is a constant, such as a ratio defined by sizes of components within the translinear comparator; and T is the junction temperature of transistors measured in degrees Kelvin. As can be observed from Equation (1), the value of the differential voltage, Vp−Vm, varies with temperature, which means that the threshold of comparison disadvantageously varies with temperature.
FIG. 2 shows a prior art translinear comparator 201. The translinear comparator 201 compares the differential voltage over the sense resistor 105 (see FIG. 1) with the internal intrinsic reference of the translinear comparator 201. The differential voltage translinear comparator 201 includes input terminals 211 and 212 and output terminal 213. The translinear comparator 201 comprises a PNP bipolar junction transistor Qp 221 and a PNP bipolar junction transistor Qm 222. The emitter of transistor Qp 221 is coupled to terminal 211. The emitter of transistor Qm 222 is coupled to terminal 212. The base of transistor Qp 221 is coupled to the base of transistor Qm 222. The translinear comparator 201 further comprises transistors M0 230 and M1 231, which are arranged in a current-mirror configuration, and transistors M4 234 and M1 235, which are also arranged in a current-mirror configuration. The collector of transistor Qp 221 is coupled to transistor M0 230. The collector of transistor Qm 222 is coupled to transistor M4 234. The translinear comparator 201 further comprises transistors M2 232 and M3 233, which are arranged in a current-mirror configuration. The source of M2 232 is coupled to the source of M3 233. The translinear comparator 201 includes a power supply having a voltage Vin 241. A bias voltage Vbias 243 biases the base of bipolar transistors Qp 221 and Qm 222. Disadvantageously, the translinear comparator 201 is temperature dependent. The translinear comparator 201 measures a difference between a voltage Vp at input terminal 211 and a voltage Vm at input terminal 212. The translinear comparator 201 senses a differential input and asserts high a flag, Vout, at output terminal 213 when the differential voltage between the inputs Vm and Vp is larger than a predetermined threshold of comparison.
By applying Kirchhoff's voltage law, it is possible to find the following equation for the input translinear loop comprising (Vp−Vm), Qp and Qm for the translinear comparator 201:Vp−Vm=VebQp−VebQm=VT*ln(Ip/Isp)−VT*ln(Im/Ism), Equation (2)where VebQp is the emitter-base voltage of transistor Qp; VebQm is the emitter-base voltage of transistor Qm; Ip is the current through Qp; Im is the current through Qm; and where Isp and Ism are constant currents used to describe the characteristics of the transistor Qp and Qm, respectively, in the saturation region and are directly proportional to the junction area of the respective transistor. By applying algebraic and logarithmic identities, Equation (2) can be re-written asVp−Vm=VT*[ln(Ip/Isp)−ln(Im/Ism)]Vp−Vm=VT*ln[(Ip/Isp)*(Ism/Im)]Vp−Vm=VT*ln[(Ip/Im)*(Ism/Isp)]
Assuming that the ratio of all current mirrors (M0/M1, M2/M3 and M4/M5) is 1:1, and if the junction area of transistor Qm is four (4) times the junction area of transistor Qp, then Ism becomes equal to 4Isp. However, regardless of the ratio in the junction areas of the transistors, Ip will be equal to Im at the threshold of comparison. Therefore, at the threshold of comparison, the preceding equation becomes:Vp−Vm=VT*ln[(1)*(4)]≈36 mV at 300° K.
The voltage of the threshold of comparison of the prior art translinear comparator 201 can be selected by preselecting a value for ‘b’. However, because VT varies directly proportionately with temperature, the threshold of comparison of the prior art translinear comparator 201 disadvantageously varies with temperature. According to equation (1), the threshold of comparison is aT*ln(b). That is,Vp−Vm=aT*ln(b)  Equation (3)where T is the temperature measured in degrees Kelvin, and, for the translinear comparator 201, ‘b’ is a constant. Specifically, for the translinear comparator 201, ‘b’ is a ratio ‘r’ of the junction area of Qm to the junction area of Qp. The ratio ‘r’ is typically selected as four (4) so that the threshold of comparison for the translinear comparator 201 becomes approximately 36 mV, which is near the upper end of the range of 0-40 mV expected across the sense resistor 105. By combining Equation (2), Equation (3) and the known relationship VT=kT/q, it can be shown that a=k/q≈8.66×10−2 mV/degree Kelvin. Therefore, for the translinear comparator 201, when b=4, Equation (3) becomesVp−Vm=(8.66×10−2)*T*ln(4)=(8.66×10−2)*T*(1.386294361)=T*0.12 mV
Considering that a typical variation of temperature for industrial applications is from −50° C. to 150° C. (223° K. to 423° K.), the preceding equation shows that the threshold of comparison for the prior art translinear comparator 201 can vary from 26.77 mV to 50.78 mV, or ±31%, which is a disadvantageously large variation.